In the Muslim world, rising against the ruler of the time counts as rebellion. By this logic, Imam Husain (a.s.) is perceived as a rebel for daring to challenge Yazid.
This shows poor understanding of religion, true qualities of a divine proof (prophet, successor) and who counts as the real rebel for daring to challenge the divine proof.
The selection and identity of divine proofs to succeed the Holy Prophet (s.a.w.a.) was cleared outlined by Prophet (s.a.w.a.) himself in the all-important Sermon of Ghadeer.
The Muslims not only heard the Sermon of Ghadeer, they submitted to it by invoking a covenant that they would always obey the divine proofs outlined by the Prophet (s.a.w.a.) in the Sermon and would never rebel against them. Meaning Yazid would always obey Imam Husain (a.s.) and never rebel against him. So how can Imam Husain (a.s.) become the rebel in Karbala. It is Yazid who rebelled against Imam Husain (a.s.) going by the Sermon of Ghadeer.
According to the following covenant recited by all Muslims present in Ghadeer, they promised to submit only to the infallible Imams (a.s.) and reject all others:
(O Prophet) we heard, obeyed, are satisfied, and are submitted to what you have conveyed to us from our Lord and your Lord about the authority of Ali, Ameerul Momineen, and the authority of the Imams from his loins.
We pledge allegiance to you in this regard with our hearts, our souls, our tongues, and our hands.
According to this, shall we live, shall we die, and shall we be resurrected.
We shall not alter, nor shall we substitute, nor shall we entertain doubt, (nor shall we deny) nor shall we distrust, nor shall we withdraw from the covenant, nor shall we breach the pact.
You advised us on behalf of Allah regarding Ali, Ameerul Momineen, and the Imams after him that you mentioned to be of your offspring from his descendants (who are): Hasan, Husain and whomever Allah shall appoint after them.
We obey Allah, and obey you and Ali, Ameerul Momineen, and his descendants, whom as you mentioned, are from your offspring from his loins after Hasan and Husain.
Al-Ehtejaaj v 1 p 56-66